The report has a specific section related to domestic abuse and the concerns officials had about going into lockdown.
"After a sharp initial increase, police callouts relating to family violence decreased to at or below levels normally observed," the report said.
It also said there has been no increase in Oranga Tamariki reports of concern.
But officials said this was unlikely a truly accurate picture.
"These are expected to be significant underestimates of the true rates of family harm, owing to the limited opportunities to report in the context of Alert Levels 3 and 4."
In particular focus of the report was the impact of children living in violent households during lockdown.
"The impact on children is particularly important because of the potential effects over the course of their lifetime," the report said.
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A separate report, also released this morning, warned Children's Minister Tracey Martin that "Children are among those most at risk of experiencing psychological trauma and behavioural difficulties after traumatic events like the Covid-19 pandemic".
Officials noted that this year's budget committed $183 million to family violence services, in recognition of the likelihood that ongoing financial hardship and associated stress may increase the risk of family violence.